Research On Constructing Magic Square Based On Partitioned Matrix

As a special matrix,magic squares have always been a hot topic for many mathematics enthusiasts to discuss and research.Especially the research results of sum-magic squares have been quite rich,but the regulations contained in this magic square are very mysterious and still need to be explored.Block matrix is a relatively important content in matrix theory,and it is also a frequently used tool for solving high-order matrix operations.Based on the research of magic square researchers,this thesis continues to study the problem of using block matrices to construct magic squares,and conducts detailed and comprehensive research on perfect magic squares.The research will be conducted from the following four parts:In the first part,introduces the research background and related research results of magic squares,perfect magic squares and block matrices,so as to determine the significance of this topic and the necessity of research,and give the framework of the dissertation.In the second part,based on the study of magic squares,a block matrix is used to construct magic squares according to the definition and related properties of magic squares.The method to construct odd-order magic squares with block matrix,the method to construct double-even-order magic squares with block matrix,and the method to construct 8n-order magic squares with 4n-order magic squares are given.In the third part,the definitions of perfect sum-magic squares are given in the form of matrix,and the problem of constructing perfect sum-magic squares with a block matrix is studied.The methods of constructing perfect and magic squares of odd and even order with block matrix and constructing perfect and magic squares of order n~2 with n-order magic square are obtained.In the fourth part,the definition of perfect product magic square is given in the form of matrix and the block matrix construction method for perfect product magic square constructed by perfect sum-magic square is given.